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The binary pulsar J0737-3039 is the only known system having two observablepulsars, thus offering a unique laboratory to test general relativity andexplore pulsar physics. Based on the low eccentricity and the position withinthe galactic plane, Piran & Shaviv (2004, 2005) argued that pulsar B had anon-standard formation scenario with little or no mass ejection. They have alsopredicted that the system would have a very slow proper motion. Pulsar timingmeasurements (Kramer et al. 2006; Deller et al. 2009) confirmed thisprediction. The recent observations of the alignment between the spin of pulsarA and the binary orbit is also in agreement with this scenario. Detailedsimulations of the formation process of pulsar B enable us to show that itsprogenitor, just before the collapse, was a massive O-Ne-Mg white dwarfsurrounded by a tenuous, 0.1-0.16 M_sun, envelope. This envelope was ejectedwhen the white dwarf collapsed to form a neutron star. Pulsar B was born as aslow rotator (spin period ~ 1 s) and a kick received when the pulsar formedchanged its spin direction to the current one. This realization sheds light onthe angular momentum evolution of the progenitor star, a process which isstrongly affected by interaction with the binary companion. The slow propermotion of the system also implies that the system must have undergone a phaseof mass transfer in which Star A shed a significant fraction of its mass ontoB.

Binary Pulsar J0737-3039: Evidence for a new core collapse and neutron star formation mechanism